HIGH ANGLE BOUNDARIES FORMED BY GRAIN

Risa National Laboratory,

9 August

Laboratories,

Livermore,

CA 94550,

DK 4000. Roskilde, Denmark

1996: accepted 25 Nocember

1996)

Abstract-Deformationof metals from medium to high strains introducessignificant changes in themicrostructureand the texture. The microstructureevolves into a lamellar structure with boundariesofsmall to medium misorientationangles mixed with high angle boundaries.The latter category consistsof deformationinduced boundariesplus the original grain boundaries.The number of deformation

induced high angle boundaries is significantly larger than the number of original grain boundaries.Mechanisms for the formation of the deformation induced boundaries are suggested based on grainsubdivision processes which can lead to formation of different texture componentswithin an original grain.The distributionof their misorientationsis estimatedbased on these mechanisms.This estimate iscomparedto experimentalfindings for Al, Ni and Ta deformed to large strain by rolling or in torsion.This estimate and the findings are discussed and good support is established for the basic assumptionthatgrain subdivision accompaniedby a strong texture evolution can lead to a very significant increase in thein a deformed metal. These findings provide the essential physicalfraction of high angle boundariesbackground for the construction of theoretical models for the distributions. C 1997Acta Metallurgica Inc.

1. INTRODUCTIONHeavily cold worked metals are subdivided by grainboundariesand dislocationboundarieswhich arearranged in a lamellar or subgrain structure [lb3].The frequency and distributionof these boundariesdeterminesthe propertiesof the deformedmetal,includingthe flow stress, texture, recrystallizationbehaviorand the formability.A comprehensivereview of the general microstructureand texture forthe large strain state of metals was last given in 1980in Ref. [4].The boundariesin heavily cold worked metalsoriginate not only from grain boundariespresent inthe undeformedmetal, but also from dislocationboundaries which form during plastic deformationingrains that are subdividedinto regions that aresmaller than the original grain size. Qualitativelyithas been known that these boundarieshave a largeangular spread and that the misorientationacrossmany boundaries is of the magnitude characteristicofordinary high angle boundaries[2]. A quantitativeanalysis of this angular spread has, however, onlyrecentlybeen possibleby the introductionofsemi-automaticand automaticmicroscopictechniques for the determinationof local crystallographicorientationson the micrometerand submicrometerscale [e.g. 5-101.As a result, a frameworkfor the formationofdislocationboundariesduring plastic deformationhas been formulated[e.g. 111. This frameworkhasbeen supportedby many quantitativeexperimentalobservationsof a variety of metals [e.g. 51. Both this

framework and experimental

in this paper.

results will be discussed

2. PREVIOUS WORKThe developmentof boundaries with a large spreadin misorientationshas been known qualitatively sincethe discoveryof grain break-upby Barrett andLevenson [e.g. I]. Further, it has been shown that themisorientationacross many of these boundaries is ofa magnitude characteristicof high angle boundaries,e.g. through X-ray, optical and electron microscopictechniques [14]. High angle boundariesare definedas those with angles above 15-20 [12]. Because thesize scale of these boundary spacings is frequently lessit is difficultto obtainthan one micrometer,quantitativemicrostructuraland crystallographicdata. Thus there are but a handful of reports thathave observed and measured individual high angledeformationboundariesfollowing medium to largestrain deformation.These include the observationsinwire drawn Fe-Si [2], an unstable Al single crystal[ 131, frictionfollowingchanneldie deformationdeformed Cu [14], torsion deformed Al [15], rolledAl-Zr-Sialloy containingparticles [ 161, aluminumrolled to intermediatestrains [17] in heavily rollednickel [18], and heavily rolled aluminum [19, 201. Astatistical analysis of the expected grain boundariescomparedto the observedhigh angle boundariesshows that most of these high angle boundariesareformed by the deformationprocess at the placeswhere grains subdivide and are not original grainboundaries[ 181. These different observationsshow

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that high angle boundaries

formed during deformation are common to a diverse set of materials andconditionsfrom single crystals to polycrystals,purematerials,alloys and particle containingmaterials,f.c.c. and b.c.c. crystal structures;different deformation modes; and different deformationtemperatures. Many of these observationshave shown thatthe number of high angle boundariesformed acrossa grain dependson the crystal orientation.Forexample, some crystal orientationsmaintaintheiraverage orientation with increasing deformationandare thus called stable. Certain symmetric orientationshave the possibility of rotating to more than one endorientationduring deformationand are thus calledunstable.Stable single crystalsdeveloplow tomedium sized misorientations,while unstable singlecrystals develop high angles [13, 21-251. For polycrystals earlier observationshave shown an effect ofgrain orientationon the subdivision with high angleboundariesin coarse grained samples [26, 271.3. DEFORMATION INDUCED HIGH ANGLEBOUNDARIES3. I. D<formation

microstructures

andgrain subdivision

Extensive experimental observations

show that keydislocationstructuresare commonto a range ofmetals,alloysand deformationmodes.Thesedislocationstructures have been analyzed within acommon framework for the evolution of microstructures during cold deformation.This frameworkisbased on a subdivisionof grains by deformationinduced dislocationboundarieswhich at 10~ andmedium strains have been separated into two groups:(i) geometricallynecessaryboundaries(GNBs)separatingcrystallitesthat deformby differentselections of slip systems and/or different strain orstrain amplitudesand (ii) incidentaldislocationboundaries(IDBs) formed by the trapping of glidedislocations[28-331. It has been observed that with(a)

SUBDIVISION

MECHANISMS

increasing strain the misorientation

angle across thetwo types of boundary increases and that the spacingbetween the boundariesdecreases.At large strain this evolution leads to structurescomposedof dislocationboundarieshaving a widerange of misorientationsand having spacings in thesubmicrometerrange. With increasing strain it is alsoobserved that there is an increasing tendency for thedislocation boundaries to reorient from a typical cellblock structure into a lamellar structure (see Fig. 1showing a schematic representationof this change).In the typical cell block structure the GNBs includemicrobands(MBs) and single dense dislocation walls(DDWs) that surround blocks of equiaxed cells. In atypical lamellar structure at large strain, the lamellarboundaries(LBs) sandwich thin layers of cells andsubgrains oriented along the material flow direction.3.2. Formation

of high angle boundaries

The continued subdivision

of grains into crystallites surrounded by dislocation boundaries leads to alargeorientationspreadbasedon dislocationaccumulationprocesses. The formationof complexdislocationboundariesindicatesan operationofdifferentslip systemcombinationswithintheindividual crystallites. As a result, different parts of agrain may rotatetowardsdifferentstable endorientations.If such end orientationsare not too farapart, the grain subdivision will lead to a scatter inthe macroscopic texture. However, the individual endorientationsmay also representmajor and minortexturecomponentsandin suchcaseslargemisorientationswithin the original grain can build upduring deformation.Both the microstructuraland textural evolutionleads to the formationof dislocationboundariesinwhich a fraction may be classified by their higherangles (> 15520). Mechanismsfor the formation ofthese high angle boundariesare discussed in thefollowing.(h)

Fig. 2. Probabilitydensity functions of the boundarymisorientationangles, normalizedby the averagemisorientationangle, scale to the same function for 5-50% cr. or 6~ = 0.06-0.80. (a) Scaled probabilitydensity for IDB misorientationangles. The curve fit for all of the IDB data is given by equation (2) withCI= 3. (b) Scaled probabilitydensity for GNB misorientationangles. The curve fit for all of the GNB datais given by equation (2) with IX= 2.5 [36, 521.

3.2.1. Microstructural mechanisms. A number of

mechanismsbased on microstructuralevolution anddislocationprocesseshave been suggested for theorigin of these high angle boundaries[34, 351. Theseinclude:(i) cell block formationin which grains start tosubdivide from the beginning of deformationcreating long boundaries(dense dislocationwalls/microbands)in which misorientationsincrease steadily with increasing strain;(ii) an origin as in (i) but with an acceleratedevolutionat grain boundariesand at triplejunctions;(iii) coarse slip in S-bands or shear bands that giverise to regionsrotatedrelativeto theneighboringmatrix;(iv) coalescence of boundariesat large strain.The microstructuralmechanisms,particularly(i) and (ii), are expected to produce boundaries withmisorientationsmainly up to 15-30. It has beenfoundthatthe distributionof the boundarymisorientationangles for these dislocationmechanisms scales with the average angle of misorientationat low to medium strain accordingto a scalinghypothesis [36]. This scaling hypothesis allows us topredict the distributionof misorientationangles thatwould be created at large strain from the dislocationmechanisms.The scalinghypothesistakesthefollowing mathematicalform (an analog from Refsthe probabilitydensityof[37, 381) in whichmisorientationangles, P(Q, 0,) is expressed as:tExtrapolation

of IDB angles have not been included as

those boundarieswill contributeto the low end of theangulardistribution,which is not part of the presentproblem.

P(Q,&I = we/e:)

(1)

where 6 and B are the scaling exponents and,f(x) is

the scalingfunctionwhichis assumedto beindependentof total strain imparted to the sample; 6and b equal one when equation (1) is subject to thescaling constraints.Equation (1) implies that if oneplots &P(Q, 0,) as a function of 0/Q,, one should finda single curve, f(Q/&), regardless of the total strainimposed on the sample. This scaling behavior isshown in Fig. 2(a) and (b) for GNBs and IDBsseparately.These distributionscan be described bythe following empirical equation:

.m) =

CPr(a)

X%- exp( - c(x)

where x = e/Q,,, c( is a fit parameter and T(a) is the

gamma function evaluated at argument M. The valuec( = 3 gives a descriptionof the scaledIDBdistribution,whereas c( = 2.5 describesthe distribution of GNBs.The angulardistributionwhich followsfromequation (1) and equation (2) has been extrapolatedto large strains based on an estimate of the H,, forGNBs at cold reductions(c.r.) of 70% and 90%.tThis extrapolationuses an empirical 2/3 power lawrelationshipbetweenthe averagemisorientationangle and the strain within the scaling regime forGNBs. H,, for GNBs at 70% and 90% c.r. isestimated to be 10 and 15, respectively, accordingto Ref. [36]. This calculated distributionof anglesbased on the microstructuralcontributionsshowsthat 99% of the boundaries are less than 30 at 70%c.r. and 45 at 90% c.r. [Fig. 3(a)]. Note that in thispaper, both misorientationand disorientationareused interchangeablyto mean the minimum anglethat reflects the crystal symmetry. Disorientationis

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the wordcoinedto describea misorientationcalculated based on a minimum angle relationshipbetween crystallitesdeterminedby consideringall[39].symmetry operations3.2.2. Texture mechanisms. Of equal importanceto the originof highangleboundariesaremechanismsinvolvinggrain subdivisionand theevolution of a preferred texture during deformation,including:(i) the rotation of apreferredcrystalmation;(ii) ambiguity of sliporientationsthatwithin a grain.

subdivided grain to different

orientationsduring defor-

(40.1

0.08

contribution fromislocation accumulation

-: 0.06Q)g

0.040.020(b,

10 20 30Disorientation

40 50(deg)

60

systems for unstable crystal

lead to diverging rotations

Grains rotate to a few preferred

crystal orientationsthatare frequentlyarrangedalongacontinuousskeleton line in orientationspace. Largecrystal rotationsare required to bring the startingtextureto the final preferredtexturefor mostdeformationconditions.If a grain subdivides,theindividual crystallites within a grain may also rotatetowards the preferred end orientations[19]. Since thedifferent end orientationsmay differ by very largemisorientations,this process will thereby create veryhigh angle boundaries.The creation of the highestangle boundaries based on texture evolution will occuronly after some finite deformationwhen the preferredend texture is well developed. Recent analysis basedon local crystallographymeasurementshave shownthis relationshipbetween deformationinduced highangle boundariesand the evolutionof typical deformation textures in rolling and torsion [19, 20,401.The high angle boundaries that form as a result oftexture evolutionin subdividedgrains, may relatedirectly to the orientationof the different texturecomponents(see Table 1) and their neighbor-neighbor relationship.This relationship has been exploredfor 10 componentsand variants (cube, brass, Goss,copper, S) of the typical rolling texture of f.c.c.metals.7 These ideal componentscan give rise to44 different neighbor-neighborrelationships,eachcharacterizedby an angle/axis pair. To calculate adistributionbased on these 44 permutations,it isassumedthateachcomponenthas an equalprobabilityof being a nearest neighbor of anothercomponent.Also only the exact ideal componentisconsidered. Note that while more elaborate methodshave been employedin the past to obtain angledistributionsbased on texture orientationdistribution functions,those calculationsalso containassumptions that are not relevant for the present case[e.g. 411. Thus, the present simplificationis preferredfor illustration.The calculateddistributionof thetThe cube componentis included in this analysis because itis a major componentof the initial texture. However, therotated cube componentin Table 1 is not included, sinceit is a minor transitionarycomponentand not part of thedeformationcomponents.

Fig. 3. Predictions of probability distributions

fordisorientation angles based on a simple composite modelcombining (a) microstructure mechanisms and (b) grainsubdivision and texture evolution mechanisms.misorientationangles based on these ideal orientations are given in Fig. 3(b), and shows a range from20 to 60.3.2.3. Evolution oJ microstructure and texture.Comparing Fig. 3(a) and (b), it is apparent that verydifferentdistributionsand ranges of angles areproducedby the two types of mechanism.Themicrostructuralmechanismsproduce a peak in thedistributionat low angle ranges less than l&15,whereas the texture evolution produces a peak at thehigh angle range above 40. A combinationof the twodistributionsinto a total distribution with the correctamount of each populationwould be needed for acomplete quantitativeprediction.This combinationwould reflect that both microstructureand textureevolve and interact with each other. Methodsofcombining the distributionswill be addressed later inthe discussion section.The microstructuraland textural evolution establish a frameworkfor the evolution of deformationinduced high angle boundaries.This framework,however, needs experimentalverificationwhich isdone in the followingfor aluminum,nickel andtantalum deformed at medium to large strain. Theexperimentalsection is followed by a comparisonofthe hypotheticalangulardistributionwith thoseobserved experimentally,and includes the effect ofmaterial and process parameters.Finally, the effecton material properties of a relatively large number ofhigh angle boundariespresentin the deformedmicrostructureis discussed.

plane and rolling

The propertiesof the three materialsand thevarious deformationconditions used in this study areshown in Table 2. Thin foils for transmissionelectronmicroscopy (TEM) were made to view the samples inthe longitudinal side plane for rolling or the Z-thetaplane for torsion.(Z is the shear plane normal,theta is the shear direction.)Transmissionelectronmicroscopy and convergent beam diffraction analysisof these samples was performed.Orientationsofindividualcrystalliteswere obtainedfromtheconvergentbeam Kikuchi patterns.Crystallitesassmall as 40 nm couldbe measuredwith thistechnique. The Kikuchi patterns were analyzed usinga computer method based on the techniques in Refs[IO, 421 to obtainthe orientationmatricesforindividual crystallites. The minimum angle misorientation relationship(disorientation)between adjacentcrystallites separated by dislocationboundarieswascalculated by considering all 24 symmetry operationsfor the orientationmatrices in a standard manner,The axis/angle pairs for the disorientationswere alsocalculated. The axis/angle pairs were quantitativelyspacing

tGrain size is given as a Heyn intercept distance.

$Calculated based on the deformationkinematicsVLMiq van Mises effective strain.xx IS cross rolled.

shear

comparedto axis/anglepairs for coincidentsitelattices. The disorientationaxes were also comparedto the sample axes of the adjacent crystallites.Anegative or positive disorientationangle was assignedby considering whether the disorientationaxis is in aleft hand or right hand triangle, respectively.Measurementerrors for these Kikuchi methodsinclude errors that arise from measuring the Kikuchipattern itself and cumulative errors in the measuredorientationsdue to slight overall bending in the thinfoils. Errors in both the orientationand misorientation between adjacent crystallites based on patternmeasurementare 0.1 to I, as examinedin Refs[lo. 421. Note that orientationangle changes due tooverall foil bending are restricted by both the thicksupportingsample rim and the geometryof thesample holder and microscope.Furthermore,theseerrors were carefully examined using single crystalthin foils measured over large distances of 500 to1000 pm. Such careful measurementshowed thatcumulativeerrors in the orientationmeasurementthat would develop owing to slight foil bending areonly about 2 over 100 kirn of sample [43]. Additionalevidencefor the goodnessof TEM orientationanalyses is found in Ref. [44] in which orientationsin

AND RESULTS

4.1. E,xperirnent

Table 2. Average intercept

Crystal orientation{hk/J<uow)i

Label

Fiber linkmgthe sequence:BI, Sz. CI, SI.B:, Si, Cz, SI

tThe designationjhk/)(uw)refers either to the rollingdirection, respect&yfor torsion.

4.

B.c.c. rolling

Crystal orientation(hk/)(ucw)1_

Label

3875

and mitral spacing.

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a single crystal were measured over long distances in

the TEM and then comparedto similar measurements using scanning electron microscopy(SEM).The errors from these effects, < 1 on misorientationand < 3 on orientation,are insignificant with respectto the range of misorientationangles and to theidentificationof local orientationtype considered inthis paper.For the rolled nickel and aluminum (small grain),themacroscopiccrystallographictexturewasmeasured previously using neutron diffractionandplotted as an orientation distribution function (ODF)[20, 341. The macroscopiccrystallographictexturesfor Ta, coarse grain aluminum, and torsion deformednickel was measured using standard X-ray diffractiontechniquesand are reportedin Refs [4547],respectively.The startingtexturesrangedfromrandom to medium recrystallizationtextures for allmaterials,exceptthe coarsegrainedaluminumsample which had a strong (100) TD (transversedirection)fiber.Followingdeformation,typicaldeformationtextures developed in every case.Previousextensiveobservationsshow that keydislocation structures are common to a broad rangeofmetals,alloysanddeformationmodes[ 17, 28, 31, 32, 48-521. Furthermore,these key structures evolve withina commonframeworkformicrostructuralevolution,whichwe call grainsubdivision [28&32]. The observationsin the presentstudy are in general accord with this earlier work.However, new results have been obtained especiallyon the microstructureand local crystallographyofspecimensdeformedat medium to large strains.These results are presented in subsections 4.24.4.4.2. MicrostructureSimilar large strain microstructuresdevelop atlarge strains for this diverse group of materials andconditions. Typical for all is a composite structure oflong lamellar dislocation boundaries alternating withstrips of equiaxedsubgrains.Examplesof thesestructuresfor the three materials and three deformation modes are shown in Fig. 4(a) and (b). Sinuousstrips of many fine lamellae alternate with strips ofequiaxed subgrains and widely spaced lamellae. Themacroscopicshape of these large strain structuresreflects the direction of the imposed deformation.Thus for straight rolling and cross rolling the lamellarboundariesare nearly parallel to the rolling plane,while in torsion the lamellar boundariesare nearlyparallel to the z plane which containsthe sheardirection.The proportionof the microstructurecontainingequiaxedsubgrainscomparedto theproportioncontainingstrips of lamellar dislocationboundariesdependson the materialand thedeformationmode. For example, aluminum with itshigher stacking fault energy has a greater proportionof equiaxed subgrainsthan rolled nickel. Torsiondeformed nickel has a greater proportionof equiaxedsubgrains than does rolled nickel.

The type of structure found in between the lamellar

boundariesalso depends on the material and thestrain level. For aluminum and nickel, dislocationcells are typically found in between the lamellarboundaries. These cells are arranged one to three cellsdeep between the lamellar boundariesand a few tomany cells along their length at these large strains.Fewer cells are observed in nickel than in aluminum.For tantalum a loose network of dislocationsin aTaylor-likelattice is more commonlyobserved inbetween the lamellar boundariesthan are strings ofequiaxed cells. In all cases a string of low angleequiaxed cells within a lamellar band is punctuated ateither end by an equiaxed subgrain. These subgrainsare surrounded by very high angle boundaries and arethus very like a micrometersized grain.The boundaries introduced by deformationin theform of dislocationboundariesor as high angleboundariesare predominantlypresent as a bandedstructure of a macroscopic orientation with respect tothe specimenaxes. Examplesare the microbandstructure at low and medium strain and the lamellarstructureat large strain.For such anisotropicmicrostructuresit has been chosento use theboundarydistanceor the number of boundariesmeasured along straight lines as the structural parameters. For example, the average intercept spacing ofthese boundaries along ND (normal direction) and zdirectionsis shown in Table 2 for the variousconditions.Additionally,there are also regions filled withequiaxed subgrains (ES) or remnants of the smallerstrainmicrobandstructure.The smallerstrainmicroband structure is most prevalent in the 70% c.r.sample and is also found with a lower frequency in90% c.r. samples. No microbandsare found at 98%.The microbandstructureat these large strains isinterpenetratedby coarseslip in S-bands.The_ 5-pm long S-bands run parallel to crystallographicslip planes and directions.Frequently,lamellarboundariesare formed in regions where S-bandsintersect the microbands.It was also observed thatsome grains at 90% c.r. were traversed by regions oflocalized glide that are roughly 1-5 pm wide by20&200 pm long. In addition to the disappearanceofthe small strain microstructurefeatures, the principlechangein the dislocationmicrostructurewithincreasingstrain above 70% is the coalescenceofdislocation boundaries.Thelocalorientationmeasurementswerecomparedwith the macroscopictextures.It wasobserved that both microscopicallyand macroscopitally there is a large spread about the ideal texturecomponentswith the local orientationfalling withinthe intensity contoursof the macroscopicODFs.In such a comparisoncare should be taken owing tothe limited number of local orientationmeasurements The qualitative agreement observed, however,indicates that the sampling in the convergent beamanalysis is representativefor the specimens.

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3877

Fig. 4(a&Caption overleaf.

4.3. Disorientations and angle/axis pairsThe distributionsof the measuredboundarymisorientationsare shown in the histogramsinFig. S(a)-(f) for all of the materials and deformationmodes at strain levels above tuM = 1.4. Allof thesedistributionsinclude a wide range of angles from nearzero to 62.8. Significantly,these distributionsalsoexhibit both a large peak at small angles and a

medium sized population

at very high angles. Thepopulationat the very high angles is not observed atstrain levels at or below tvM = 1. The rotation axes forthese disorientations,plotted in the adjacent standardtriangles, are generally scattered across the wholetriangle and do not show strong crystallographicpreferences.The average spacing of the high angle boundaries,shown in Table 2 is always much less than the average

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HUGHES and HANSEN:

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spacing of original grain boundaries for all materials

and deformations.The spacing of the high angleboundaries is also smaller than a 30 deviation in theaverage grain boundary spacing, indicating that themajority of the high angle boundaries are formed bythe deformationprocess.The disorientationsacross the dislocation boundaries in adjacentcrystallitesare plottedagainstdistancewithina grainin Fig. 6(a)-(e).Thedisorientationswere measured in a line either alongthe ND for rolling, or the z axis for torsion. All ofthe orientationchanges shown occur sharply at adislocation boundary. Note the alternating nature ofthe disorientationsshowing very little cumulativeangle change over the distances considered. There isa very wide range of spacings for the high angleboundaries.While these boundariesare distributedcontinuouslythroughoutthe distancesmeasured,some clusters of high angle boundariesas well asquieter regions with small angle changes can be seen.The wide variety of rotation axes for the lamellarboundaries(Fig. 5) indicates a varied mixture ofboundary types from near twist and tilt boundaries tomixed type boundaries.The length of these high angle boundarieswasexploredby followingthe orientationsalong twoadjacent lamellar boundariesfor a long distance of40 Ltrn along the RD. These boundaries are part of astructure in which many high angle changes occurredperpendicularto the LBs. In contrast to a directionperpendicularto the LBs, mostly small angle changeswere found within the lamellar bands (Fig. 7). Highangle changes occur occasionally within a band whena small equiaxed subgrain was traversed. Of equalsignificance was the fact that the rotation axes withina lamellar band were more likely to be clusteredabout preferredaxes, in contrastto the variedrotations across the bands. Note that except for thesmall equiaxedsubgrains,one lamellarband iscomposedof orientationsaroundthe same Siorientationvariant for 40pm (Fig. 7) while theadjacent band is composedof the B, orientationvariant. Consequentlya very high angle boundary ismaintained between the two bands for at least 40 pm.Different magnitudes of angle changes were foundwithin different dislocation microstructures.Well-developed lamellar bands had larger misorientationsthandid regionsof microbands.Highangleboundaries were also frequent across the long stripsof LBs formed in a microband structure due to coarseslip along S-bands or in which micro-shearbandsoccurred within a microbandstructure. An exampleof this effect was observedin the structurerepresentedby the disorientationplot in Fig. 6(a).4.4. Local texture

distributions

The pattern of orientations

of individual crystallites is highlightedin the previous disorientation[Fig. 6(a)-(e)] by color shading regions to reflect theirassociationwith specific ideal components.A localorientation is classified as an ideal component if it has

SUBDIVISION

MECHANISMS

3879

a disorientationof less than 15- relative to the idealcomponent.An orientationnot within 15 of anyideal component is taken to be a random orientation.The ideal componentsconsideredthroughoutthepaper are listed in Table 1. The complementaryvariants of the same ideal componentwere alsodistinguished,since these variants differ from eachother by high angle rotations (e.g. 60^ about (1 11)).The most striking features in Fig. 6(a)-(e) are thelarge numberof high angle disorientationsthataccompany a very fine scale pattern of local texturecomponents.Note that most (>2/3) of the very highangle changes, >30 , in Fig. 6(a))(e) separate twodifferent ideal texture components.In contrast, onlyl/4 separate an ideal componentfrom a randomcomponentand less than l/l5 separate two randomcomponents.Remarkably,owing to the many highangle changes,nearlyall of the ideal texturecomponentsand their variants are frequently foundover a distance of just a few micrometersin all thesevarious structures. For f.c.c. rolling, the orientationscan be seen to span a wide range of the x and /Ifibersplus some randomcomponents[see especiallyFig. 6(a), (b) and (d)]. These orientationsarefrequently arranged in space so that they alternateback and forth along the length of the c( and /r fibers.Analogously,for torsion, observed orientationsspanand alternate along the {l I ~)(uz~M~) and (Ml){ 110)fibers [Fig. 6(c)]; for b.c.c. rolling all of the idealcomponentsalong the {OOl}(urn~) or (111 ](uw~)fibers are found [Fig. 6(e)]. Strikingly, this trend canalreadybe observedat a 70% c.r. (E,~ = 1.4)[Fig. 6(a)] and is maintainedwith increasing strain.At these large strains the random components werescattered throughoutthe microstructure.Althoughrandom componentscould be found in regions witheither S-bands or localized glide bands, the frequencyof the random componentswas not any higher thanelsewhere.In fact the localized glide bands weretypified by having a normal deformationtexture. e.g.copper or S.It must be noted that texture componentsof adifferent color are not always separated by high angleboundariesin Fig. 6. This result occurs as aconsequenceof the texture grouping we use that isbased on the classification of an orientationas idealif it is within I5 of the ideal, combined with the factthat adjacent ideal orientationsalong the b fiber areonly 19.4 apart.The local measurementsalso show that each of thedeformationtexture componentsis composedof avery large number of small volumes with orientationsscattered around the ideal orientations.An estimateof the size of such volumes for rolling shows that theiraverage dimension in the ND direction may be l/3 tol/5 of the reducedgrain size (Table 2). Thedimensionsin the RD and TD directions gives anaverage aspect ratio for the pancake shaped volumesof about 335. This average aspect ratio is somewhatmisleading because of the wide distribution of lengthsfor the pancake shaped volumes. Within lamellar

bands, pancake shaped volumes with aspect ratios of

lo-20are punctuatedby high angle equiaxedsubgrains with aspect ratios of 1. Another contribution to the wide variety of these aspect ratios is thetendency of high angle boundaries to cluster. Thus, adistributionof the individual volume elements thatcompose the macroscopictexture has a very largespread in size from a small fraction to a couple ofpm3.4.5.

The efects

crystal structure,

The

formation

of grain orientation,

material purity,

strain level and deformation

of

high

angle

boundaries

mode

and

sr.C-l.RD*

10

15

20

25

30

35

4u

Distance along RD (pm)

Fig. 7. Disorientationangles measured across dislocationboundarieswithin a single lamellar band in the rollingdirection.The color shading shows that similar texturecomponentsare maintainedwithin the band.

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local orientationsmay be affectedby severalparametersincludinggrain orientation,materialpurity, crystal structure, strain level and deformationmode.4.5. I. Orientation effkcts. In general the high angleboundariesare distributedwidely throughoutthedistances measured. These high angle changes occurboth in the grain centers and near original grainboundaries. At the same time, there are quiet regionswith only low to medium angle changes and regionswith clusters of high angle boundaries.For the caseof f.c.c. rolling, these quiet regions were associatedwith average grain orientationsalong the c1 fiber,includingGoss and brass components[see, e.g.Fig. 6(d)]. For b.c.c. rolling these regions wereprimarilyassociatedwith the rotated cube orientations (see, e.g., Fig. 6(e) and Ref. [53]). In no casedid these regions with low to medium angle changesextend across the whole grain width; rather theyoccupy fractions of a grain, even for the rotated cubeorientationin tantalum.In contrastto the quietareas, the clusters of high angle changes in f.c.c.rolling are associatedwith alternationsprimarilyalong the /jfiber including finely distributedregionswith the variantsof S, copperand brass plusoccasionally a Goss orientation.No clear orientationeffects could be identified for the case of torsion,although somewhat larger frequencies of high anglechanges are associated with orientationsalong the(111) fiber compared to the (110) fiber.4.5.2. Material purity and type. Similar numbersof high angle boundariesand varietiesof localorientationsare observed for a range of materialpurity from 99.999% to 99.5% (Table 2 plus Ref.[ 191). However,significantlymorehighangleboundarieswere observed in nickel than in aluminum, consistent with a finer spacing of dislocationboundariesin nickel compared to aluminum.4.5.3. Crystal structure. The different deformationtexturesthat develop reflect the differentcrystalstructures, f.c.c. or b.c.c. as expected. However, boththe b.c.c. and f.c.c. metals show similar trends withrespect to the number of high angle boundaries andtexture components.However, the average number oftexture componentsin b.c.c. tantalum, 24, is smallerthan that for f.c.c. 2-7, at the same strain. Thisdifference is partly related to the stability of therotated cube grains in the tantalum and the largernumberof ideal texturecomponentsfor f.c.c.compared to b.c.c.4.5.4. Grain size and shape effects. The grain sizesin this study ranged from medium-small(44 pm) tomedium-large(150 p). Within this grain size range noobservableeffects of either the initial or deformedgrain size were observed.For example, the sameaverage spacing of high angle boundaries is observedfor aluminum with two different initial grain sizes(Table 2). Both aluminum samples showed the similarvarieties of high angle boundariesand local texturecomponents.All of these suggest a minor role of the

SUBDIVISION

MECHANISMS

initial grain size. It must, however, be noted that

neither very large grain nor small grain specimenshave been examined.4.5.5. Strain level. The formation of most of thevery high angle boundariesoccurs within a verylimited strain range. At strain levels between 50 and60% c.r. (t,, = 0.8 to l), all of the observed highangle boundaries are less that 25-30. Strikingly withincreasingstrainto 70% c.r. (tvM = 1.4), themaximum angle increases to 62.8. The frequency ofhigh angle boundariesalso increases in this narrowstrain range. With a further increase in strain from70% c.r. (ttM = 1.4) to 90% c.r. (c,~ = 2.7) there issome increase in the number of very high angleboundaries.However, none occurs above 90% c.r.This developmentof high angle boundaries matchesthe overall trend for dislocationboundarieswithincreasing strain in this strain range. For example,Table 2 shows that the spacing of the high angleboundaries in nickel decreases with strain at a similarrate comparedto the dislocationboundaries.Thisdecrease is quite different from that of the steepdecrease of the original grain boundariesduringrolling (Table 2). The torsion data for the high angleand the dislocationboundaryspacing match therolling data (Table 2).The variety of local orientationsincreasesintandem with the formationof the very high angleboundaries.At the very largest strains it is observedthat there is a slight increase in the number of randomcomponentsin the structure.defor4.5.6. Deformation mode. The differentmation modes, torsion and rolling, produce differentpreferred textures and different macroscopicshapechanges.Both modes producean active textureevolution that includes large rotations.In spite ofthe differences,very similar average spacings areobserved for both the high angle boundaries and thedislocation boundaries (Table 2). However, in torsionthe grain shape does not become as flat as that inrolling (by a factor of 7). Consequently,the similarhigh angle spacingsbetweenthe two types ofdeformationmode results in the creation of 334 highangle boundaries per grain in rolling compared to 27in torsion,on average.The similaritiesin thedistributionof the high angle boundaries and in thediversity of local texture components is also shown bycomparing Fig. 6(b) and (c).5. DISCUSSION5.1.

Boundary formation

The observed microstructural

subdivision leads tothesubdivisionof thecharacteristictexturecomponentsinto small volumeelements.Theseobservations support the hypothesis that deformationinducedhigh angle boundariesarise from bothmicrostructuraland textural evolution.The currentexperimentsprovideadded information to that previously published on the origins of

HUGHES and HANSEN:

GRAIN

high angle boundaries.

This informationincludes therelative importance of each mechanism and the rangeof high angles created.5. I. 1. S-bands. The S-band structure provides avery visual illustrationof a mechanismby whichdeformationstructures can develop many long highangle boundariessubdividingthe original grains.At strains ranging from 50 to 90% c.r., variousdistributionsand arrangementsof S-band clustershave been observedwithin grains includingbothevenly spaced strips and groups of strips. The firstarrangementwould lead to evenly spaced high angleboundaries,while the latter to clusters of high angleboundaries. The observed range of angles formed bythis mechanismare in the medium to higher anglerange from 10 to 30 with 20 boundariesmosttypical. This mechanismis very common and thenumber of high angle boundaries that it produces ishigh. However, it is unlikely that very high angleboundariesgreater than 40 could be produced bythis mechanism alone. A similar effect is found for theobservedshear bands, but their frequencyin themicrostructureis less than that for S-bands.5.12. Cell blocks. Cell block formation results inhigh angle boundaries that are generally less than 35,as discussed in Section 5.2.5. I .3. Coalescence ofboundaries. At large strain, ahigh proportionof boundaries are combined togetheras the number of boundaries across a grain is reducedwith increasingstrain. The resultant angle changeacross the coalesced boundarieswill be quite variedand depend on either the alternatingor cumulativecharacterof their angle/axispairs. Calculations,based on experimentaldata, show that high angleboundariesformed by coalescenceare rare. Thisresult is due to the great variety of boundary axes andthe diversity of neighbororientationsthat makesstrictly cumulative misorientationsuncommon[35].5.1.4. Grain-grain interactions. The current datasets provide an estimate of the relatively modestproportionof high angle boundariesarising fromgrain boundary effects. Of particular importanceisthe torsion data [Fig. 6(c)] in which 28 high angleboundariesare spread across the distance of onegrain and thus two grain boundary regions. Based onthe experimentalobservationsof grain boundaryregions [54-561 and simulations[57], only 20% ofthese boundariesshould be associatedwith grainboundaryinteractions.The remaining80% mustoccur for other reasons. The high angle boundariesfound in rolling also spread across the whole grainwidth and are not associated with the grain boundaryregions. For example, the measurementsin Fig. 6(a)(nickel 70% cr.), that begin on the right in the middleof an original grain and end on the far left at a grainboundary,show that the high angle boundariesarecontinuouslydistributedacross the grain.5.1.5. Special initial orientations. There is a clearorientationdependenceon the formationof highangle boundaries. However, the importance of special

SUBDIVISION

MECHANISMS

3883

orientationsin creatinghigh angle boundariesdepends on the starting texture of the material. Whilethis mechanismis a potent source of high angleboundariesin polycrystalswith strongstartingtextures such as cube, its potency diminishes with anincreasinglyrandomstartingtexture since fewerregions are near these special orientations.For theweaklytexturedmaterialsin this study,thismechanism is only of small to moderate importance.5.1.6. Etolving texture. A more potent source ofhigh angle boundaries may be found if one considersthe whole of texture evolutionand not just theevolutionof special orientations.Large crystalrotations are required to bring the starting texture tothe final preferred texture.The above hypothesis is supported by consideringcrystal rotationsusing a Taylor model. Duringdeformation,an initially random grain is reorientedalong a path in orientationspace that is defined bythe rotationor reorientationvelocityfield inorientationspace [58]. Since both the magnitude anddirectionof this velocity dependson location inorientation space, each part of a subdivided grain willhave a somewhat different reorientationvelocity anddirection.While this rotationfield is generallysmooth, there are regions in which a small change inorientationcauses a reasonably large change in thevelocity.Largedifferencesin velocitybetweenadjacent crystallites in a grain result in the evolutionof large differences in orientation and misorientation.As texture evolves, a random subdivided grain willapproachregions with large velocity changesasfollows.The characteristicstructure of the rotation fieldcauses crystals of any general or random orientationto be funneled into orientation streams flowing to oneend orientation.However, as the crystal volumes ofa subdivided grain are swept along these reorientation streams, the volumes rotate near one or moresurfaces in orientationspace that separate streamswith branchingpaths to different end orientations.Because a grain has been subdivided,it contains arange of crystal orientations,each with its ownrotation rate and direction, since the latter depend onthe current orientationwith respect to the deformation axes. Consequently,different parts of a grainwill approach these branching paths at different timesand locations in orientationspace. These differenceswill cause some parts of a grain to follow one branchwhile others will follow a different branch, therebycreating some very high angle boundarieswhen thedifferent end orientationsare reached. The initialcrystal orientation and deformationmode will dictatethe degree of subdivision necessary to cause this largescale splitting. For special orientationsalready nearthe surfacesin orientationspace that separatebranchingpaths,grain subdivisioninto regionsseparated by only a couple of degrees of misorientation is required. In contrast, for orientationsthat arefarthest away from these branches, grain subdivision

3884

HUGHES and HANSEN:

GRAIN SUBDIVISION MECHANISMS

into regions separated

by 20 rotationangles isrequired,based on the 45 periodicityof thesebranches.The creation of high angle boundariesbased ontexture evolution will occur only after some finitedeformationwhen the preferred end texture is welldeveloped.This delay occurs because an initiallyrandom grain will only be swept near these brancheswhen it is near to the end orientationor fiber oforientationscharacteristicfor the deformation.5.2. Comparison of the hypothetical distributionsmisorientation angles with experiment

of

The predictionbased on the addition of distributions in Fig. 3 based on both microstructureandtexture provides good qualitative agreement with theexperimentaldistributionsin Fig. 5. While thesimplified model representedin Fig. 3 captures themain featuresobserved,it is not meant to bequantitative.For example, the distributionpeak atthe small angle range occurs at a somewhat larger lowangle in the predictions than in the experiments. Thismoderate difference is indicative of the interactionsbetween the dislocation and the texture mechanismswhich we know exist, but do not account for in thesimple model. Also the contributionto the distribution from the dislocation mechanismsis based onan extrapolationof both the average angle and thescaling observed at small to moderate strains. Thisextrapolationis acceptable for strains below c,~ = 2.7(90% c.r.), althoughit slightly over-predictstheaverage angle from the dislocation contribution.From the experimentalresults, we know thatdislocationboundariesform which subdividetheoriginal grains and that a preferred texture evolves.Thus both dislocationprocesses and texture evolution occur togetherin the experiments.This isreflected in the distributionof misorientationdata inFig. 5, clearly showing a large peak in the distributionat lower angles and a second populationat highangles.The dislocationmechanisms[Fig. 3(a)]contribute most to the peak observed at small angles,but only 1% of those boundariescontributeto theangle range greater than either 30 or 45 at 70% and90% c.r., respectively.The experimentsshow asignificantly larger percentage of lo-25% for the highangles This high angle population is in a similar rangeto the broad peak formed by preferredtextureformationin a subdividedgrain [Fig. 3(b)]. Thetexturemechanismscontributeto only a smallportion of the distributionat the lowest angle range.Combiningthe two distributionsin the simplifiedmodel of Fig. 3 to obtain a more quantitativepredictionwould require the incorporationof thegrain subdivisionas described by Fig. 3(a) into acrystal plasticity model. This incorporationis easiestto envision, for example, in a finite element basedplasticity model. As texture evolves within subdividedgrains in the polycrystalmodel, a fraction of highangle boundaries will grow at some of the boundaries

created by grain subdivision.

Which of the boundaries becomesa high angle boundaryas textureevolves will depend on the local crystal orientationand the angle/axis pair of the boundary misorientation.The predictionsbased on an addition of distributions establish the essential physical backgroundrequired for the developmentof theoretical models ofmisorientationdistributionsat large strains. Thesemisorientationdistributions,when combinedwiththe spatial distributionof dislocationboundaries,provide the basis for quantifyingdislocationstructures and stored energy for inclusion into constitutivemodels of material deformation,texture formationand recrystallization.5.3. Texture

and texture spread

Notably, the microstructural

subdivision of grainsinto fine crystalliteshavinga large spreadinorientationsdoes not lead to new major texturecomponents,indicating that Taylor-likekinematicsare valid on average. Instead, subdivisioncreatessome minor componentsand a spread in the texture.This spread increases the width and decreases theintensityof the texture peaks in the ODF. Inthe following we estimate this spread based on themicrostructure.Regions separated by both high angleboundariesand low angle boundariescontributetothis spread. The local orientationsreflect the effect ofthe microstructureon the texture.Thus,themicrostructuralcontributionto the observed texturespread is estimatedby averagingthe difference(disorientation)betweenthe measuredindividualorientationsand the orientationsof the nearest idealtexture components.Those values, shown in Table 3,are similar for all of the rolled samples and rangebetween 11 and 13 at a 90% cold reduction.Incontrast, the spread in the torsion textures, 16.9, ismuch larger than those for rolling, consistent with thedifferencesin the respective macroscopictextures.These data also show an increasing texture spreadwith increasing large strain. However, this may ormay not be a real trend as the differences are withinone standard deviation. More data would be neededto determine if this trend is correct.Table

90% cr. (LM = 2.7)

purity)90% cr. (C.M= 2.7)purity)

12.9

90% x.r. (fvM = 2.7)

11.0

70% cr. (c,\, =

90% cr. (C\M=95% cr. (r,, =98% c.r. (F,M =(CM = 4.0)

texture

13.1

HUGHES and HANSEN:

GRAIN SUBDIVISION MECHANISMS

Calculated deformationtextures frequently predictmuch higher intensities at the peak intensity points inthe ODF as well as much narrower angular spreadsin intensityabout those peaks than is found inexperiments[59]. Smoothingfactors used in recenttexture simulations to reduce the sharpness of thosecalculatedtextures to the approximatelevels observed in experiment, include 7.5 [.59] and 7-8 [60].However, larger smoothingfactors from 9 to 17,based on Table 3, may be more representativefortextures developing at large strains. As an additionalapplication of the present data, the orientation spreadowing to the microstructurecan be introducedintopolycrystalmodels to predict the formationof thehigh angle boundaries.5.4. Effect qf material

and deformation

parameters

Several parameters have an effect on the formation

of high angle boundaries.Strain level has a largeeffect that has also been previously observed [2, 31.The crystal orientationis also importantand theobservationof clustering of high angle boundaries atlarge strain indicatesthat some (unstable)grainorientationshave a much larger tendency to becomesubdividedby high angle boundariesthan other(stable) orientations.This also agrees with previousobservations[I, 27, 521. In contrast, the deformationmode, crystal structure and material purity may havesecond order effects.As regards grain size, it has been found to have noeffect on the spacingbetweenthe high angleboundaries(see Table 2). This is in contrast to theobservationsin Refs [26, 271, where the subdivision ofgrains has been studied in crystallographicallyetchedlongitudinalsections of fine and very coarse grainedcopper cold-rolled 83%. The average layer thicknessfor volumes of different crystallographicorientationshaving andecreasedfrom - 17 pm in specimensinitial grain size of -3000 firn to -2.5 pm inspecimens having an initial grain size of 40 pm. Toclarify this issue experimentsare under way onspecimens with a larger difference in grain size thanin the present study.Finally, it is a general observation that most of thehigh angle boundaries are created in the strain rangeat whicha crystallographictextureis rapidlyevolving. It appears that the parametersassociatedwith a very active texture evolution have the largestinfluence on the creation of the very highest angleboundaries.5.5. &i?ect on recovery and recrystallizationIn generalthese effects are suggestedto besimilar to those encounteredwhen the originalgrain size is reduced.In general the high angleboundariesact as sinks for dislocationsduringannealingand as nucleationsites [61]. Anotherimportanteffect is related to the fine distributionof texture componentsin the deformed microstructure whichmay affectthe growthof grains

3885

during recrystallization.Specific orientation relationships may result in acceleratedgrowth,but inmost cases the migrationof high angle grainboundarieswill be slowed down or stoppedbyorientationpinning. Orientationpinning arises byimpingementbetweena growinggrainand adeformedcrystalliteof similarorientationthatleads to the replacementof a mobile high angleboundarywith a much less mobilelow angleboundary [61].6. CONCLUSIONSDeformationof metals from mediumto largestrain introducessignificant changes in microstructure, texture and local crystallography.These changesare illustrated by experimentalexamples for differentmetals deformed by different processes. The following conclusionsare drawn:The microstructureevolvesinto a lamellarstructure of dislocation boundaries of small andmedium angles mixed with high angle boundaries. The number of the latter is significantlylarger (e.g. about 3-5 times in rolling, 27 times intorsion)than the numberof originalgrainboundaries.?? The macro-textureevolves into a typical deformation texture containinga number of texturecomponents.Local crystallographicmeasurements show that the volume fractionof theindividualtexture componentsis composedofmicrometerand submicrometersized volumesdistributed throughoutthe deformed microstructure.?? The distributionof misorientationsacross lamellar boundarieshas been estimatedbased onassumptionsthat those boundaries are formed byevolving grain subdivision processes, which canlead to different texture componentswithin anoriginal grain. The estimated distributionsare ingood agreementwith those determinedexperimentally at large strain by automatedKikuchidiffraction techniques.?? Theformationof high angle grain boundariesduring plastic deformationleads to a deformation induced reduction in grain size. This grainrefinementwill have an effect both on themechanical and on the thermal behavior of thedeformed metal.